---
vault_clearance: SAFE
halo:
  classification: PUBLIC
  confidence: HIGH
  front: "05_Project_LENG"
  custodian: "The Architect"
  created: 2025-12-21
  updated: 2026-03-25
  wing: READY
  containment: "None — physics framework with public-release directory"
---
# LENG: The Geometric Foundation of the Standard Model

## Principles of Fundamental Constants from Zero Parameters

**Status: ✅ Universe Successfully Compiled**
- 92 predictions (build); 87 Theorems (paper v12)
- Zero free parameters
- Canonical state: [BOUNTY_BOARD.md](BOUNTY_BOARD.md), `lotus-universalis/build.py`, `public-release/lotus/`

### Vault spine & sister projects (01–05)

**Spine:** [Lab protocol](../README.md#lab-protocol) · [Vault bounty board](../BOUNTY_BOARD.md) · [Session (vault-wide)](../WORLDLINE.md) · **This project:** [BOUNTY_BOARD.md](BOUNTY_BOARD.md) · [WORLDLINE.md](WORLDLINE.md) · **[All projects hub →](../README.md#project-workflow-index-all-links)**

**Sister projects:** [01 World](../01_Project_World/README.md) · [02 Triage](../02_Project_Triage/README.md) · [03 Technomancer](../03_Project_Technomancer/README.md) · [04 Constitution](../04_Project_Constitution/README.md)

**Full folder & authority map (what file owns what):** [_MAP.md](_MAP.md) — use this when grep finds multiple trees or mirrored paths.

## Memory and sovereignty

> *Without body, one has no agency. Without mind, they have no freedom. Without memory, one has nothing.*

**LENG** is **memory as theorem**: derivations, scripts, and the bounty board are how physics survives any single author or model — **mind** proves, **memory** (repo + session logs) holds the chain honest. Lab-wide: [Memory and sovereignty](../README.md#memory-and-sovereignty).

## Project Entry (Unified)

- Canonical vault onboarding: [../README.md](../README.md) (single root entry)
- Canonical Daemon (information graph): [../06_Project_Daemon/README.md](../06_Project_Daemon/README.md) — `06_Project_Daemon/_daemon_v3.py`, `songs/`
- Quick structural check from the Daemon tree: `cd ../06_Project_Daemon` then `python _daemon_v3.py _test_leng` (or your graph name)

### Where LENG topics live (routing)

| Looking for… | Go here |
|----------------|---------|
| **Folder authority**, staging vs release, what not to edit | [_MAP.md](_MAP.md) |
| Task state, predictions, script **Where** | [BOUNTY_BOARD.md](BOUNTY_BOARD.md) |
| Derivation chains, **Script:** / **Derivation:** per result | [WORLDLINE.md](WORLDLINE.md) |
| Heat kernel, math→physics, cascade map | [public-release/SPECTRAL_MAP.md](public-release/SPECTRAL_MAP.md) |
| Agent onboarding, tiers, Database Protocol | [START_HERE_FOR_AGENTS.md](START_HERE_FOR_AGENTS.md) |
| Lotus API, contributing scripts | [lotus-universalis/CONTRIBUTING.md](lotus-universalis/CONTRIBUTING.md) |
| **Name collision:** “Ji Leng” in [02 Triage](../02_Project_Triage/README.md) | Fictional character — **not** this physics project. |
| Universe String / DNS (separate from SM constants) | [01 World](../01_Project_World/README.md) |

## Start Here

**Follow the protocol in each project.** Canonical procedure: [README § Lab protocol](../README.md#lab-protocol). This project's board: [BOUNTY_BOARD.md](BOUNTY_BOARD.md). Session log: [WORLDLINE.md](WORLDLINE.md). Where to put scripts: `public-release/verification/`, `public-release/lotus/`, or `public-release/nonunified/`. LENG-specific procedure (tiers, Database Protocol, path conventions): [START_HERE_FOR_AGENTS.md](START_HERE_FOR_AGENTS.md) §2–2b.

- **Agents & collaborators (single entry):** [../README.md](../README.md) — routing, daemon-first runtime, LENG workflows (Unification, Identification, Discovery), BOUNTY_BOARD rules, and task handoff protocol.
- **Derivations and scripts:** Each result’s derivation chain and script path live in [WORLDLINE.md](WORLDLINE.md) (per breakthrough: **Derivation:** and **Script:**). The bounty board “Where” column points to those same scripts and to the session doc.

### Workflows (Unification, Identification, Discovery)

**Full workflow rules:** [../README.md](../README.md) — single entry for agents and collaborators; read §6 (LENG workflow) there.

| Workflow | Purpose | When |
|----------|---------|------|
| **Unification** | Merge overlapping docs; archive superseded content (no file left at original path); renumber IDs so one canonical source remains. | Duplicate IDs, conflicting counts, or two docs claiming "single source of truth." |
| **Identification** | Orient (read key docs), find gaps (missing derivations, stale claims), log them on the bounty board. | New agent joining; after a major session; periodic hygiene. |
| **Discovery** | Pick a gap from the board, claim it (set IN PROGRESS, Assigned), say where you'll put scripts, then try it. | When you want to work on a bounty. |

**Where things live:** Scripts → `public-release/verification/` (and `public-release/lotus/` for the engine). Derivation map (heat kernel, math→physics, full cascade) → [public-release/SPECTRAL_MAP.md](public-release/SPECTRAL_MAP.md). Per-result derivation chains and script paths → [WORLDLINE.md](WORLDLINE.md) (**Derivation:** and **Script:** in each breakthrough block). Task state and "Where" column → [BOUNTY_BOARD.md](BOUNTY_BOARD.md).

**Work in lotus:** Design new scripts to work *with* lotus (use `lotus.quick()`, `lotus.Universe()`, `lotus.full_cascade()`, etc.). New or exploratory scripts that are not yet part of the core go in **`public-release/nonunified/`**; when stable and agreed, unify them into `public-release/lotus/` (or move to `verification/` if derivation-only). See [../README.md](../README.md) and [lotus-universalis/CONTRIBUTING.md](lotus-universalis/CONTRIBUTING.md).

**Documentation cleanup (Unification):** When LENG docs become repetitive or fragmented: (1) **Assess** overlaps and identify the canonical file. (2) **Fuse** duplicate narrative into one source. (3) **Cleanup** by moving superseded files to `_archive/` and removing them from the original path (no redirect file); keep README and Folder Authority Map clear so "scripts here, mapping in the map file" is obvious.

---

## Folder Authority Map (Current Maintenance)

Use this map to avoid editing mirrored or historical trees by accident:

- **Canonical release/runtime tree:** `public-release/` — run scripts from here (`verification/`, `tools/`, `papers/`). **Staging for new scripts:** `public-release/nonunified/` — develop here; unify into `lotus/` or move to `verification/` when ready.
- **Canonical task tracker and prediction state:** [BOUNTY_BOARD.md](BOUNTY_BOARD.md) — OPEN/SOLVED, status, Assigned, Where (script paths). Check IN PROGRESS and Assigned before claiming a bounty.
- **Canonical agent entry:** [../README.md](../README.md) — Unification, Identification, Discovery workflows; board rules; check-before-claim.
- **Canonical derivations and script links:** [WORLDLINE.md](WORLDLINE.md) — each breakthrough block has **Derivation:** and **Script:** where applicable; board “Where” points here and to the same scripts.
- **Canonical derivation map (heat kernel + math→physics):** [public-release/SPECTRAL_MAP.md](public-release/SPECTRAL_MAP.md) — single doc: Heat Kernel Keystone, Quick Reference by layer, full cascade. *Archived (fused here):* heat_kernel_derivation_table.md → `_archive/stale_root_docs/`; MATH_TO_PHYSICS_QUICK_REFERENCE → `_archive/docs/`.

- **Historical / superseded docs:** `_archive/stale_root_docs/` (reference only). `_archive/docs/` (archived public-release docs).
- **Research/historical materials:** `public-release/papers/`, `_archive/` (do not treat as release runtime defaults).

---

## Derived Constants from Spectral Geometry

Project LENG derives all fundamental constants from the spectral geometry of the $S^5/\mathbb{Z}_3$ orbifold. Every value is a consequence of the manifold's symmetry, not a measured input.

| Parameter | LENG Geometric Formula | Predicted Value | PDG/measured | Residue (Δ) | Status |
| :--- | :--- | :--- | :--- | :--- | :--- |
| **Proton Mass** | $m_p = 6\pi^5 m_e(1 + \frac{10}{9}\frac{\alpha^2}{\pi})$ | 1836.1527... | 1836.1526... | < 10⁻⁷ | ✅ Locked |
| **Cabibbo Angle** | $\lambda = \sum \vert \eta(\chi_k) \vert = 2/9$ | 0.2222 | 0.2250 | 0.0028 | ✅ Hurricane |
| **Strong Coupling** | $\alpha_s(M_Z) = \pi^2 - \lambda_1 = \pi^2 - 5$ | 0.1174 | 0.1179 | 0.6σ | ✅ Verified |
| **Higgs VEV** | $v/m_p = 2/\alpha - 35/3$ | 246.22 GeV | 246.22 GeV | 0.005% | ✅ Locked |
| **Higgs Mass** | $m_H/m_p = 1/\alpha - 7/2$ | 125.10 GeV | 125.25 GeV | < 0.15% | ✅ Locked |
| **Lepton Koide** | $K = (1+r^2/2)/3 \to 2/3$ | 0.6666... | 0.6666... | Exact | ✅ Geometric |
| **Koide Phase** | $\delta = 2\pi/3 + 2/9$ | [Resulting Mass Triplet] | e, μ, τ masses | < 0.007% | ✅ Locked |
| **Wolfenstein A** | $A = \lambda_1/d_1 = 5/6$ | 0.8333 | 0.826 | < 1% | ✅ Verified |
| **CP Phase γ** | $\gamma = \arctan(2\pi^2/9)$ | 65.49° | 65.6° | < 0.2% | ✅ Locked |
| **Neutrino Split** | $\Delta m^2_{32}/ \Delta m^2_{21} = d_1^2 - p = 33$ | 33.0 | 32.58 | 1.3% | ✅ Verified |
| **Top Yukawa** | $y_t(\Lambda_{UV}) = 1$ | 174.1 GeV (UV) | 172.69 GeV | QCD Run | ✅ Inevitable |

---

## Core Axioms of the Framework

The framework is built upon three non-negotiable geometric truths:

1. **Axiom of the Manifold**: The internal space of the universe is a $S^5/\mathbb{Z}_3$ lens space.
2. **Axiom of Spectral Monogamy**: A quantum state's capacity for spectral distortion is conserved ($\sum e_m = 1$).
3. **Axiom of the Ghost Gap**: Gauge structure and confinement emerge from the spectral hole at $\ell=1$ where $d_{inv}=0$.

---

## Falsification Protocol

Following the "Code as Law" principle, we do not perform "tests"; we seek to **falsify** the foundation.

- **Belle II Proof**: The LENG prediction for the Tau mass is $1776.985$ MeV. If Belle II precision results fall outside $1776.9 \pm 0.01$, Axiom 1 is dead.
- **LHC Higgs Scan**: Any significant deviation in the $m_H / v$ ratio from the spectral invariant 1/2 will trigger a reconstruction of the Higgs Sector geometry.

---

## Complete Prediction Inventory

The table above shows key highlights. For the complete auditable chain and current state:

- **[BOUNTY_BOARD.md](BOUNTY_BOARD.md)** — Open questions, SOLVED list, script locations (canonical task/prediction state). Before claiming a bounty: only pick OPEN with Assigned = —; set IN PROGRESS and Assigned when you start.
- **[WORLDLINE.md](WORLDLINE.md)** — Derivation chains and **Script:** paths per result (canonical source for “how” and “where in code”).
- **[SPECTRAL_MAP.md](SPECTRAL_MAP.md)** — Single canonical derivation map (Heat Kernel Keystone + Math→Physics quick ref + full cascade). *Archived:* MATH_TO_PHYSICS_QUICK_REFERENCE.md → `05_Project_LENG/_archive/docs/`.
- **[public-release/verification/](public-release/verification/)** — Executable verification scripts
- **Build / counts:** run `lotus-universalis/build.py` or see `lotus-universalis/lotus.json` meta

---

## Navigation: The Theorems

- [Geometry](public-release/papers/markdown/Supplement_I_Geometry.md)
- [Lepton Sector](public-release/papers/markdown/Supplement_II_LeptonSector.md)
- [Baryon Sector](public-release/papers/markdown/Supplement_IV_BaryonSector.md)
- [Verification](public-release/verification/)
- [Falsification](public-release/tools/falsification/)

---

> *"There are no knobs in the universe. Only geometry."*